Arithmetic Series Application

1. Which of the following is a formula for arithmetic series?

• A) 𝑆_𝑛 = 12 (𝑎₁ + 𝑎_𝑛)

• B) 𝑆_𝑛 = $\frac{1}{2}$(𝑎₁ + 𝑑)

• C) 𝑆_𝑛 = $\frac{n}{2}$(𝑎₁ + 𝑎_𝑛)

• D) 𝑆_𝑛 = $\frac{n}{2}$(𝑎₁ + 𝑑𝑎_𝑛)

2. Find the sum of the first 12 terms of the arithmetic sequence 4, 11, 18, …

• A) 610

• B) 510

• C) 530

• D) 410

3. Find the sum of the first 15 terms of the arithmetic sequence 17, 12, 7, 2, …

• A) 270

• B) 287

• C) −287

• D) −270

4. The sum of the first 12 terms of an arithmetic sequence is 606. What is a₁ if the last term is 67 and d is 3?

• A) 64

• B) 54

• C) 34

• D) 44

5. The second term of an arithmetic sequence is −16 and the eighth term is 8. What is the sum of the first 10 terms?

• A) -15

• B) -20

• C) 15

• D) 20

6. Find the sum of the first 40 terms of the arithmetic sequence if the first term is 16 and the tenth term is 70.

• A) 5,320

• B) 1,720

• C) 2,200

• D) 6,320

7. Find the sum of the first 15th terms of the arithmetic sequence whose nth term is 𝑎_𝑛 = 5 + 3𝑛.

• A) 435

• B) 860

• C) 870

• D) 430

8. The first term of an arithmetic sequence is 8, the last term is 56 and the sum is 416. Find the number of terms.

• A) 13

• B) 12

• C) 11

• D) 10

9. If the first n terms of the A.S 24, 20, 16,... are added, how many of these terms will be added to get a sum -60?

• A) 35

• B) 30

• C) 25

• D) 15

10.A yaya has a starting annual salary of P60,000 with a yearly increase of P3,600. What is her total income for 5 yrs.?

• A) Php 672,000.00

• B) Php 552,000.00

• C) Php 336,000.00

• D) Php 276,000.00